It is planned to develop a theoretical model for the screening of chronic diseases in order to determine optimal periodic screening programs. The ideal optimal program specifies: the number of examinations, the age at which the first examination should start and the optimal inter-examination schedule. Optimal screening programs will be found for a general class of utility functions which is a function of the probabilities of: case detection at examination and that of being incident between examinations. The theory will be applied to determine the optimal screening exams for breast, cervix and colon cancer. The model is very general and will be applicable to other chronic and infectious diseases in which there is need for a program of periodic examinations. The economic consequences of applying these models to specific diseases are potentially very large. It is likely that it will result in considerable savings in cost and, at the same time, increase the efficacy of such programs.